Questions tagged [quantum-chemistry]
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346 questions
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Emission and absorption of photons by atoms in atomic spectrophotometry
My question is about the interaction of photons with the electrons of atoms.
In atomic absorption spectrophotometry the atoms' electrons absorb photons which make the outer electrons "jump" ...
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Modelling quantum harmonic oscillator for oscillations of simple linear molecules (IR spectroscopy)
My question is how to model the oscillation of atoms in simple molecules (for instance $Cl_2$ or other gases) when exited by infrared photons.
I mean how to get theoretically their IR spectrum ...
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Angular orientation of exact solution of the Hydrogen Schrödinger Equation
I am currently trying to get a better understanding of the basis sets used for computational quantum chemistry and as a start read ch.6 on the exact solution of the Schrödinger equation of the ...
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WKB tunneling probability calculations
I'd like to calculate the WKB tunnelling probabilities from different vibrational levels. I hope the question is not too chemical.
I have a compound which undergoes a chemical reaction. For the ...
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How much does the ligand field splitting energy increase upon oxygen binding in hemoglobin? [duplicate]
In hemoglobin, iron transitions from a high-spin state ($S = 2$) in deoxygenated heme to a low-spin state ($S = 0$ or $S = 1/2$) upon oxygen binding. (This is the cause of the change in magnetic ...
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Does there exist a version of the Slater-Condon rules for a sum of Slater determinants?
The Slater-Condon rules are useful in working out the non-zero single and double electron matrix elements.
For example if $\vert \Psi \rangle = \frac{1}{\sqrt{2}} \vert \phi_{1s}^{\alpha}(1) \phi_{2s}^...
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What is the algorithm for determining what energy is spent on in a quantum chemical reaction? [closed]
The law of conservation of energy tells us that the sum of the potential and kinetic energy of a system is constant.
Suppose two atoms/molecules collide (each has its own velocity vector) and an ...
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What does 'spin-adapted' mean?
I've seen this term everywhere but I haven't actually seen an explanation for what it means. I've seen it be applied to operators or other quantities, such as a density matrix $\rho(x, x')$, or ...
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What is the smallest bound cluster of Helium-3 atoms?
Helium-4 can form an extremely weak dimer. It is a barely-bound halo state in which most the molecule's wave-function is in the classically forbidden region.
Helium-3, however, has no dimer. (Edit): ...
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Is electron correlation in Quantum Chemistry a consequence of many-body entanglement?
Electron correlation is largely defined in Quantum Chemistry as the set of properties that the celebrated Hartree Fock Approximation cannot model accurately. One popular example is the phenomenon ...
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Is the electron pair in an orbital entangled?
In the video "Bird navigation: The Quantum Around You. Ep1", Dr. Andrea Morello seems to imply that the electron pairs in atomic orbitals are entangled and will exhibit properties of ...
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How to derive the expression for derivative couplings on using the Born-Oppenheimer expansion?
I am trying to understand the derivation for the non-adiabatic coupling (NAC) elements as presented in Conical Intersections Electronic Structure, Dynamics and Spectroscopy by Wolfgang Domcke and ...
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What are the linear combination of slater determinant for three electrons on three different spatial orbitals? [closed]
I read the following link : https://chem.libretexts.org/Courses/Pacific_Union_College/Quantum_Chemistry/08%3A_Multielectron_Atoms/8.06%...
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How Does Our Current Understanding of QFT Affect Chemistry and Biology?
Quantum Field Theory (QFT) faces significant challenges, particularly in dealing with non-perturbative phenomena such as bound states in QED with nuclei and confinement in QCD. While perturbative QFT ...
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Charge transfer broadening effect in solid state absorption spectra
What is the range of a broadening effect of a charge transfer absorption? Is it tenth's of eVs or different?
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Fermions in a infinite 1D well and spinorbital
I am learning quantum chemistry. To have a comprehensive understanding of the Slater determinant, I studied the classical problem of two indistinguishable particles in a 1D box with infinite barriers. ...
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Other than approximating the total energy of the system, what other information does the Hartree-Fock method provide?
In the Hartree-Fock method, one computes the energy of an interacting quantum-many body system, described by $H$, via taking a non-interacting trial ground state, $|\psi_{\mathrm{HF}}\rangle$, and ...
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Could the scattering of molecules lead to bond compression?
Suppose you were to send a fast moving binary molecule (such as H-H) at another large target atom A such that the molecule is aligned with the direction of its travel towards the target atom. In other ...
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Boron triplet states
Is it possible to achieve the following electron configuration of triplets in Boron, if you were to align the spins by means of electric field, or magnetic field, or just electromagnetic radiation?
[!...
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Difference between GW gap and BSE gap. How does net charge play a role?
The energy gap from BSE (GW-BSE) is just the lowest optical excitation energy.
The energy gap from GW, from what I read, is the electron affinity (energy of adding an electron).
I suppose this means ...
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Total ground state energy calculation of an electron-ion system using plane wave basis sets
Recently I have begun working on a project which involves constructing a "simple" density functional theory (DFT) code using a plane wave basis set in Python. My first step has been to try ...
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Can Hartree-Fock determinant WLOG taken to be real?
For a many-electron Hamiltonian $H$, a Hartree-Fock determinant is a Slater determinant $\Psi$ that minimizes the energy $\frac{\langle\Psi,H\Psi\rangle}{\langle\Psi,\Psi\rangle}$. In general, $\Psi$ ...
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Flatband with our Moire Physics
Is there any material Class available where the lattice vectors are in the order of several nm instead of Angstrom? I am looking for some exotic not well studies lattice class which can be ...
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Why ionization energy of oxygen dips moving from nitrogen to oxygen if the total spin decreased?
How does spin-orbit splitting also affect this or anomalous zeeman effect or decrease in spin when you move from Nitrogen to Oxygen?
Bad Teacher: The addition of the second electron into an already ...
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Placement of nucleons in the shell model for odd-even nuclei
The question I'm trying to answer is this:
What are the spin and parity predicted by the shell model for 37
20Ca (in order of increasing
energy the order of states is [1s1/2
, 1p3/2
, 1p1/2
][1d5/2
, ...
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Conflicts on spin directions in the molecular term symbol for O$_2$
We know that the ground-state electron configuration of O$_2$ is $K K (\sigma_g 2s)^2 (\sigma_u 2s)^2 (\sigma_g 2p_z)^2 (\pi_u 2p_x)^2 (\pi_u 2p_y)^2 (\pi_g 2p_x)^1 (\pi_g 2p_y)^1$. The spins of the ...
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Muonic Hydrogen Dissociation
Is the dissociation energy of a muonic molecular hydrogen ion the same as an ordinary molecular hydrogen ion? Would the cross-section for dissociation be the same as an ordinary molecular hydrogen ion?...
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Exchange Particles for IMF
Quantum field theory describes forces as being mediated by a field (e.g. gluon field for strong force, electromagnetic field for electromagnetic force). These are often modeled as a mediating boson ...
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How to calculate total angular momentum $L$ of partially filled $p$-orbitals?
Why has $^1D$ configuration lower energy than $^1S$ ?
Hund's second rule says that for two configurations with
the same multiplicity, the configuration with the highest total orbital angular momentum $...
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What is the relation between the Adiabatic Approximation used in quantum chemistry and the one given in QM textbooks?
I am an aspiring quantum chemist and have come across two vastly different versions of the Adiabatic Approximation when studying Quantum Mechanics from the perspective of physics and chemistry ...
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Angular momentum uncertainty principle and the particle on a ring
By considering a particle on a ring, the eigenfunctions of $H$ are also eigenfunctions of $L_\text{z}$:
$$\psi(\phi) = \frac{1}{\sqrt{2\pi}}e^{im\phi}$$
with $m = 0,\pm 1,\pm 2,\cdots$. In polar ...
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Carbon dioxide vibration
Can we induce antisymmetric stretching vibration in carbon dioxide molecules by collision with nitrogen molecules in air at standard temperature and pressure?
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The relation between state function and molecular orbitals
In some chemistry classes I was taught the (seemingly usual) 'tale of exactly two atoms' that form bonding and anti-bonding states in the LCAO-theory (similar to this question). I've not seen the ...
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Thermodynamics and Gibbs energy
The equation for the Gibbs free energy is: $\Delta G = \Delta H - T\Delta S.$
$\Delta H$ is the amount of energy difference between the initial state (characterized by $U_{i}$, $S_{i}$, and $V_{i}$) ...
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How is energy conserved in formation of chemical bonds?
I understand that when an H$_2$O molecule is formed, it has lesser total energy than the constituent (2H and O) atoms. I also understand that the potential energy (PE) will be reduced when the atoms ...
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Measurement of dipole electric field generated by a polar molecule
I'm trying to understand the nature of polar molecules. Have there been experiments where we can say to have actually measured the dipole electric field generated by a polar molecule such as hydrogen ...
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Is Hartree-Fock energy minimisation an iterative or a Lagrange undetermined process?
Suppose the following is about a quantum system of N electrons.
In the canonical Hartree-Fock method, the goal is to find single - electron orbitals $\phi_{1}, ...,\phi_{N}$ such that $\langle \psi_{...
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Number of summations for a Hartree-Fock (single-orbital as basis functions) method
The Hamiltonian for a quantum $N$ - body system:
$$\hat{H} = - \frac{1}{2}\sum_{i}^{N}\nabla_{i}^{2}-\sum_{m;i=1}^{N}\frac{z_{m}}{r_{im}}+ \sum_{i;j>i}\frac{1}{r_{ij}}.$$
The first two terms can be ...
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Can a matter enter do work without being consumed up? [closed]
I had a tricky question in mind. So, I wanted to use the example of Catalysts (In chemical reactions) as an example. It's said that when catalysts enter a chemical reaction, they're Never consumed up. ...
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Where is the kinetic energy functional error in the exchange-correlation functional of DFT?
The Kohn-Sham DFT energy functional is:
$$E[\rho]=T^S[{\varphi_i}]+J[\rho]+M[\rho]+E^{xc}[\rho]$$
with the kinetic energy functional of non-interacting electrons $T^S$, the Hartree functional $J$, the ...
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Why using real wave functions instead of complex ones?
I have already seen similar questions asked in the site (like this or this), but I don't feel that my question has been fully addressed.
I understand that orbitals $np_x$ and $np_y$ are linear ...
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On completeness of a set of commuting operators for homonuclear diatomic molecules
The electronic Hamiltonian for a homonuclear diatomic molecule is $$\hat{H}=-\sum_{i=1}^N \frac{\hbar^2}{2m} \nabla^2_i -\sum_{i=1}^N \frac{Z_Ae^2}{4\pi\epsilon_0|\vec{r}_i-\vec{R}_A|} -\sum_{i=1}^N \...
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Density functional theory: logical steps from Hohenberg-Kohn theorems to Kohn-Sham equations
I'm trying to learn density functional theory (DFT), using Engel & Dreisler, Sholl & Steckel, and Wikipedia as 3 different sources of information. Although I have made some progress, I am ...
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Deducing physical properties of substances with physics
Inspired by this question (Why does amount of protons define how matter is?) I’m wondering how one can deduce the physical properties of an element with physics. For example, it is known that sodium ...
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Gibbs energy calculations for compounds
I am studying machine learning during my master's degree and have a simple task. I am using the FactSage Pure Substance Database (https://www.crct.polymtl.ca), which provides a list of phases for a ...
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Is it possible to calculate the average kinetic energy of an atomic orbital in an heavy atom? [closed]
I am trying to calculate cross sections for electron impact ionization in heavy atoms (Xe and I) using a BEB technique. To do this I need, for each occupied orbital, occupancy number, binding energy ...
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What is the physical origin of two Hydrogen atoms repelling at short distance?
Consider two isolated $\rm H$ atoms. They can be in different spin states, but the different states are degenerate. Now move these $\rm H$ atoms together. Now the singlet state will become ...
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Where does this (hydrogen molecule energy) graph come from?
I was thinking about the good old question of 'Why do molecules have lower energy than the atoms?'
And in a video (around 6:15), this good old energy graph is shown, which is stated as the 'answer' to ...
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Dirac equation for solving $\rm H^-$ anion
Let's try to solve 1 dimensional Dirac equation for a $\rm H^-$ anion. If you solve the time independent Dirac equation and allow motion of electrons only in the $x$ axis you get:
$$-\chi\frac{d\Psi_{...
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How do nuclear physicists know for certain if a very short-lived nucleus has been formed (a new isotope)?
Some very short-lived nuclides (sometimes called 'resonances') are nevertheless considered to have actually existed, if only very very briefly....
How do nuclear physicists know the isotope actually ...
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